Thanks for the suggestions, Tango and BlackJohn.
So.. I tried mixing acid and liquid dish detergent. A few detergent and maybe 1/4 cup of the previously-diluted acid. It was still too runny; I wanted to get a consistency somewhere between thin and heavy syrup.
Next I tried mixing in some regular wheat flour from the kitchen. I'd read online somebody suggested saw dust, but all I have is coarse pine shavings (animal bedding stuff) and flour seemed similar. It made a nice batter, a little lumpy, but spread on the plate well. I was working in the sun at the time and the batter dried fast so I misted it frequently with water from a spray bottle. That all was relatively ok; the only problem was that it didn't actually take the scale off the plate.
Finally I resorted to building a bath. I got some chain attached to the bottom side of the plate, laid down a sheet of OSB covered with polyethylene, and set the plate down on some spacers. I tried a few different arrangements and materials for spacers, but there was always somewhere that the plate seemed to be touching the plastic and wood. It wouldn't have had good acid contact there and I set the project aside to think about it a little longer.
After few days I realized I could set the plate down right side up with no spacers and pour the acid over the top instead.
On Saturday I did just that. I welded four pegs of 1/4" wire to the edges of the plate so that a chain could be slipped over these for lifting the plate either side up, then used the skid loader with backhoe arm to move the plate.
I had a gallon and a half of diluted acid and poured that over the plate. It turned out the bath wasn't quite as level as I'd intended it to be and the acid pooled a bit at one end. There wasn't enough liquid so I added more acid straight from a fresh jug, a little here and a little there.
That's potent stuff.
I was working outdoors and there was a breeze but it frequently changed direction. More than once I caught just a whiff of the fumes and had to hold my breath and step (even farther) away. I worried I was going to have to call the fire department hazmat to come and drain it off back into the jugs for me.
Fortunately after 20 minutes or so the fumes subsided significantly and I was able to stand near the plate. With an acid brush on the end of an 8 foot extension pole I picked up acid from the pool at the end and pulled it across the plate. The scrubbing action really helped get the rust and scale off. The whole thing was done in about 40 minutes.
I drained the acid off into a bucket, again lifted the plate with the skid loader, and rinsed it with water. I used a rag to dry it and another to wipe on WD-40 to minimize rusting. That worked pretty well.
I now have significant rust staining on the concrete. It's like the Cat in the Hat story about the pink spots. That's a problem for another day.
Lessons learned: hydrochloric acid is absolutely amazing at stripping mill scale and rust off a plate that's been stored outside who-knows-how-long. But 20 square feet is way too much open surface for working with acid that strong. I should've had supplied air or at least an acid-rated respirator. If I had treated the plate face down there would have been much less acid surface exposed to the air, but removing air bubbles underneath would have been difficult and I'd have been unable to brush to accelerate the scale removal.
The plate came out looking very nice. Not that one can tell from the pictures above -- something was wrong with the auto exposure setting in my camera and they came out very dark. Here's a photo of the table back in the shop with another non-cleaned plate laying on top for reference.
I'd rather not keep treating this with WD-40 to keep rust away, though -- I don't want to be constantly getting that on clothes, gloves, and projects that come across the table. Will phosphoric acid work to keep further rust away on steel that isn't rusty yet? It's so dry here that maybe I'll be fine to degrease the plate and simply keep it dry. Rust hasn't been a problem on bare/untreated steel on my bus, after all.